Beginning Algebra, 11th Edition

4.1

system of linear equations
(linear system)

solution of a system

solution set of a system

set-builder notation

consistent system

inconsistent system

independent equations

dependent equations

4.5

system of linear inequalities

solution set of a system of

linear inequalities

KEY TERMS

1.Asystem of linear equations
consists of
A.at least two linear equations with
different variables
B.two or more linear equations that
have an infinite number of
solutions
C.two or more linear equations
with the same variables
D.two or more linear inequalities.

2.Aconsistent systemis a system of

equations

A.with one solution

B.with no solution

C.with an infinite number of

solutions

D.that have the same graph.

3.Aninconsistent systemis a system

of equations

A.with one solution

B.with no solution

C.with an infinite number of

solutions

D.that have the same graph.

4. Dependent equations
   A.have different graphs
   B.have no solution
   C.have one solution
   D.are different forms of the same
   equation.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

4.1 Solving Systems of Linear Equations

by Graphing

An ordered pair is a solution of a system if it makes all
equations of the system true at the same time.

To solve a linear system by graphing, follow these steps.

Step 1 Graph each equation of the system on the same
axes.

Step 2 Find the coordinates of the point of intersection.

Step 3 Check. Write the solution set.

Is a solution of the following system?

Yes, because and are both true,

is a solution.

Solve the system by graphing.

The solution checks, so

is the solution set.

1 3, 2 2 51 3, 2 26

x+y= 5

2 x-y= 4

1 4,- 12

4 + 1 - 12 = 3 2142 - 1 - 12 = 9

x+y= 3

2 x-y= 9

1 4,- 12

QUICK REVIEW

CONCEPTS EXAMPLES

ANSWERS

SUMMARY

CHAPTER 4

1.C;Example: 2.A;Example:The system in Answer 1is consistent. The graphs of the equations intersect at exactly
one point—in this case, the solution 3.B;Example:The equations of two parallel lines make up an inconsistent system. Their graphs never
intersect, so there is no solution to the system. 4.D;Example:The equations and are dependent because their graphs are
the same line.

4 x-y= 8 8 x- 2 y= 16

1 2, 3 2.

2 x+y=7, 3 x-y= 3

x

y

0

5

–4

2 5

(3, 2)

x + y = 5

2 x – y = 4

(continued)

286 CHAPTER 4 Systems of Linear Equations and Inequalities

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